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ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A linear mixed finite element scheme for a nematicEricksen–Leslie liquid crystal model ∗
F.M. Guillén-González, J.V. Gutiérrez-Santacreu
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 47 / Issue 5 / September 2013

Published online by Cambridge University Press:

30 July 2013, pp. 1433-1464

Print publication:

September 2013
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In this work we study a fully discrete mixed scheme, based on continuous finite elementsin space and a linear semi-implicit first-order integration in time, approximating anEricksen–Leslie nematic liquid crystal model by means of aGinzburg–Landau penalized problem. Conditional stability of this schemeis proved via a discrete version of the energy law satisfied by thecontinuous problem, and conditional convergence towards generalized Young measure-valuedsolutions to the Ericksen–Leslie problem is showed when the discreteparameters (in time and space) and the penalty parameter go to zero at the same time.Finally, we will show some numerical experiences for a phenomenon of annihilation ofsingularities.